Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the exponents n a x n b = n a+b

Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the exponents n a x n b = n a+b To divide powers with the same base, subtract the exponents n a  n b = n a-b

Exponent Law DescriptionAlgebraic representations To multiply powers with the same base, add the exponents n a x n b = n a+b To divide powers with the same base, subtract the exponents n a  n b = n a-b To determine the power of a power multiply the exponents (n a ) b = n ab

Exponent Law DescriptionAlgebraic representations The power of a product is equal to the product of the powers (m x n) a = m a x n a

Exponent Law DescriptionAlgebraic representations The power of a product is equal to the product of the powers (m x n) a = m a x n a The power of a quotient is equal to the quotient of the powers mnmn () a = manamana

Exponent Law DescriptionAlgebraic representations The power of a product is equal to the product of the powers (m x n) a = m a x n a The power of a quotient is equal to the quotient of the powers Zero exponent x 0 = 1, x  0 mnmn () a = manamana

Exponent Law DescriptionAlgebraic representations The power of a product is equal to the product of the powers (m x n) a = m a x n a The power of a quotient is equal to the quotient of the powers Zero exponent x 0 = 1, x  0 Negative Exponents x -n = mnmn () a = manamana 1xn1xn

(4x 3 y 2 )(5x 2 y 4 ) Solution (4x 3 y 2 )(5x 2 y 4 ) means 4 * x 3 * y 2 * 5 * x 2 * y 4 We can multiply in any order. (4x 3 y 2 )(5x 2 y 4 ) = 4 * 5 * x 3 * x 2 * y 2 * y 4 = 20x 5 y 6

Solution 6a 5 b 3 3a 2 b 2 6a 5 b 3 3a 2 b 2 means 6363 a5a2a5a2 b3b2b3b2 xx = 6363 a5a2a5a2 b3b2b3b2 xx 6a 5 b 3 3a 2 b 2 = 2a3b2a3b2a3b2a3b

Solution means x2z3x2z3 x2z3x2z3 * = = x2z3x2z3( )2)2)2)2 x2z3x2z3( )2)2)2)2 x2z3x2z3( )2)2)2)2 x2x2z3z3x2x2z3z3 x2x2z3z3x2x2z3z3 * x4x4z6z6x4x4z6z6

c -3 * c 5 Solution c -3 * c 5 = c -3+5 Same methods apply if some of the exponents are negative integers = c 2

m 2 * m -3 Solution m 2 * m -3 = m 2 +(-3) Same methods apply if some of the exponents are negative integers = m -1

(a -2 ) -3 Solution (a -2 ) -3 = a (-2)(-3) Same methods apply if some of the exponents are negative integers = a 6 Remember exponent law #2 ( power of powers)

(3a 3 b -2 )(15a 2 b 5 ) Solution (3a 3 b -2 )(15a 2 b 5 ) means 3* 15 * a 3 * a 2 * b -2 * b 5 We can multiply in any order. Same methods apply if some of the exponents are negative integers (3a 3 b -2 )(15a 2 b 5 ) = 3* 15 * a 3 * a 2 * b -2 * b 5 = 45a 5 b 3

Solution 42x -1 y 4 7x 3 y -2 means 42 7 X -1 x 3 y 4 y -2 xx = = 6x -4 y 6 42x -1 y 4 7x 3 y -2 42x -1 y 4 7x 3 y X -1 x 3 y 4 y -2 xx = 6y 6 x 4 Positive Exponents Same methods apply if some of the exponents are negative integers

(a -3 b 2 ) 3 Solution (a -3 b 2 ) 3 means a (-3)(3) * b (2)(3) (a -3 b 2 ) 3 = a (-3)(3) * b (2)(3) = a -9 b 6 = b6a9b6a9 Positive Exponents Same methods apply if some of the exponents are negative integers

CLASSWORK PAGE 294 #3-8 #9 (e,f,g,h,I,j) #10 – 13 Page 295 #18, #20